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Voltage-SOC balancing control scheme for series-connected lithium-ion battery packs
Journal of Energy Storage 25 (2019) 100895
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Voltage-SOC balancing control scheme for series-connected lithium-ion battery packs
T
⁎
Tiezhou Wu, Feng Ji , Li Liao, Chun Chang Hubei Key Laboratory for High-efficiency Utilization of Solar Energy and Operation Control of Energy Storage System, Hubei University of Technology, Hubei, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Voltage balancing control scheme SOC balancing control scheme Reconfigurable equalization circuit Cell
The basis for determining whether the cell needs to be balanced is generally the voltage or SOC (state of charge), the voltage balancing control scheme is simple but performs poorly, the SOC balancing control scheme performs well but needs to estimate the SOC of all cells. Based on the analysis why existing naive approaches are not effective for voltage balancing control scheme, the voltage-SOC balancing control scheme is proposed, which has the advantages of simple of voltage balancing control scheme and well performance of SOC balancing control scheme. By utilizing the difference of voltage of cell and SOC of battery pack, the difference of SOC between two cells can be obtained indirectly, and the transition from voltage balancing control scheme to SOC balancing control scheme can be realized, while the advantages of voltage balancing control scheme and SOC balancing control scheme are retained. The 4 experiments designed show that the estimated errors of the difference between the SOCs of the two cells are 0.24%, 5.3%, -5%, and 0.8%, respectively, which proves the excellent performance of voltage-SOC balancing control scheme.
1. Introduction Lithium-ion batteries are widely used in a variety of applications, including electric vehicles, energy storage systems, due to their high energy density, long cycle life and low self-discharge rate [1]. A number of battery cells are usually connected in series in order to supply higher voltage and higher power to the load in a wide range of applications, while significant efforts are made by designers to select the battery cells such that they are as identical/matched as possible, the battery cells will still have mismatches in practice due to manufacturing tolerances, different self-discharge rates, uneven operating temperature across the battery cells, and nonuniform aging process, among others. Such inevitable differences within battery cells will drift apart through cycling and could potentially lead to overcharging or over discharging, It is clear that such non-uniformity limits the battery capacity and may even cause safety issues. Therefore, to properly maintain all cells balanced is of significant importance for enhancing battery life [2–5]. Mounting research efforts have been devoted to investigating efficient cell equalizers, attentions have been also focused on the control scheme and topological structure of equalization system (see reviews [6–9]), advantages and disadvantages of various types of cell equalizers are summarized in [10,11]. The basis for determining whether the cell needs to be balanced is generally the voltage or SOC, the voltage of cell
⁎
is relatively easy to obtain, but it is greatly affected by factors such as working conditions, making it difficult to provide accurate parameters for the equalization system [12]. SOC balancing control scheme is less affected by the working state of the cell, and its equalization performance is related to the accuracy of SOC estimation [13]. In order to obtain accurate SOC of cell, it is often necessary to use complex algorithm to estimate the SOC of each cell in the battery pack, which makes the SOC balancing control scheme has disadvantages such as large amount of calculation and complexity, the SOC estimation algorithm are discussed in [14,15]. To verify the performance of the proposed equalization circuit or equalization method, most papers use the SOC balancing control scheme, however, they often ignore complex SOC estimates and consider the SOC of each cell to be known and accurate [16–19]. But in practice, the shortcomings of the SOC balancing control scheme cannot be ignored. A lot of work has been done on the shortcomings of the voltage balancing control scheme and the SOC balancing control scheme. Kim et al. used the terminal voltage to estimate the SOC by establishing a battery model [20]. He et al. and Feng et al. improve the performance of voltage balancing control scheme by increasing the OCV (open circuit voltage), polarization voltage, capacity, and other parameters [21,22]. In addition, Han et al. develop computationally efficient methods to estimate the battery cell SOC [23]. Model predictive control methods have shown better performance but require
Corresponding author. E-mail address: [email protected] (F. Ji).
https://doi.org/10.1016/j.est.2019.100895 Received 25 June 2019; Received in revised form 8 August 2019; Accepted 8 August 2019 Available online 20 August 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
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massive computational resources and time [24]. The run-to-run control method proposed by Tang et al. is easy to implement and has good performance [25]. In this paper, a voltage-SOC balancing control scheme is proposed, which can indirectly estimate the difference between the SOCs of the cell through the terminal voltage and the SOC of battery pack. It combines the advantages of simple and better performance, and also avoids the disadvantage of large amount of calculation of SOC balancing control scheme and poor performance of voltage balancing control scheme. This paper provides three contributions. 1) First, based on the reconfigurable equalization circuit, why the voltage balancing control scheme provides the error parameters for the equalization system is further analyzed. 2) Second, a voltage-SOC balancing control scheme is proposed and compared with the voltage balancing control scheme and the SOC balancing control scheme. 3) Third, the performance of the voltage-SOC balancing control scheme is verified by extensive experiment results. 2. Reconfigurable equalization circuit Compared with the traditional equalization circuit, the reconfigurable equalization circuit has the advantages of high balanced conversion efficiency and can extend the life of the battery pack [26]. Based on the reconfigurable equalization circuit, this paper analyzes the shortcomings of the voltage balancing control scheme and verifies the superiority of the voltage-SOC balancing control scheme. In this section, we use SOC balancing control scheme to briefly introduce the working principle of reconfigurable equalization circuit. The detailed introduction of reconfigurable equalization circuit can be referred to [27–29]. As shown in Fig. 1, for the cell Bn, its discharge (charge) state is controlled by the switches Sn1 and Sn2. For example, while Sn1 is ON and Sn2 is OFF, cell Bn is in a discharging (charging) state, and while Sn1 is OFF and Sn2 is ON, cell Bn is isolated from the battery pack.
Fig. 2. Cell Bn is isolated from the battery pack when the pack is discharged.
At T1, suppose that the SOC of cell Bn is lower and the SOC of cell B1 is higher, the difference between the SOCs of the two cells is given by (1)
ΔSOCT 1 = SOCB1 − SOCBn
Where SOCB1 and SOCBn are the SOCs of cell B1 and cell Bn, respectively. To make the SOC of cell Bn and cell B1 the same, that is, ΔSOCT1 = 0, when the pack is discharged, let Sn1 OFF and Sn2 ON, as shown in Fig. 2. As shown in Fig. 2, cell Bn is isolated from the battery pack, but the remaining cells are powering the load. If the current of the pack during T1-T5 is shown in Fig. 3, where the current is positive for charging and negative for discharging, I1, I2, I3 and I4 are the current of T1-T2, T2-T2, T3-T4 and T4-T5, respectively. T1-T2: Cell Bn is isolated from the pack (as shown in Fig. 2), and its SOC remains unchanged, but cell B1 is discharging, its SOC will decline, and the SOC of cell Bn is closer to that of cell B1 (assuming that the SOC of cell B1 is still higher than that of cell Bn at T2). T2-T3: Since the current is 0, the difference between the SOCs of the two cells does not change. T3-T4: The pack is charged, and cell Bn will be connected to the battery pack. Just like cell B1, its SOC will increase, and the difference between the SOCs of the two cells does not change. T4-T5: The pack is discharged, and cell Bn will be isolated from the pack, similar to TI-T2. Then, during T1-T5, the SOC of cell B1 is decreased by ΔSOCB1n more than the cell Bn.
ΔSOCB1n = −
1 ( QB1
T2
∫T1
ηI 1dt+
T3
∫T 2
ηI 2dt+
T4
∫T 3
0dt+
T5
∫T 4
ηI 4dt ) (2)
Where QB1 is the capacity of the cell B1, η is the coulombic efficiency. Refer to (2), the current during T3-T4 is 0, because during charging, cell Bn will be connected to the battery pack without isolation, so at T5, the difference in SOC between cell B1 and cell Bn is given by
ΔSOCT 5 = ΔSOCT 1 − ΔSOCB1n
Fig. 1. Reconfigurable equalization circuit. 2
(3)
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Fig. 3. The current of the pack during T1-T5.
If ΔSOCT5 = 0, the equalization system has completed the equalization task for the cell Bn. If the current during T1-A is large enough that the SOC of cell B1 decreases is equal to the SOC difference between cell B1 and cell Bn, cell Bn will be connected to the battery pack because their SOC is the same. Through the above analysis, it can be known that when the battery pack is discharged, the circuit will isolate the cell with a lower SOC. Similarly, when the battery pack is charged, the circuit can also improve the consistency of the battery pack by isolating the cell with a higher SOC. The current direction could change significantly with time in many battery applications, so that the cell that is isolated during discharge needs to be connected to the battery pack if the current direction changes, although it is not well balanced, as shown in Fig. 3, the equalization can be completed after multiple equalization.
Where Up is the polarization voltage, can be calculated as
Cp
(6)
Refer to (5) and (6), Up is given by t
t
Up (t ) = Up (0) e− R1C1 + IR1(1 − e− R1C1 )
(7)
Refer to (5) and (7), the terminal voltage U is not only related to the SOC of the cell (refer to (4)), but also related to such as current I, ohmic resistance R, the state of cell (such as discharging, resting), so that the terminal voltage U does not reflect the SOC of the cell well. Considering that the inconsistency of the cell parameters is mainly due to the difference in the using process, the difference in polarization voltage drop is much smaller than the difference in ohmic voltage drop of the cell [30]. For simplicity and clarity, it is considered that the cells in the battery pack have the same polarization voltage under the same working conditions.
3. Disadvantages of voltage balancing control scheme In this section, we will analyze the shortcomings of the voltage balancing control scheme applied to the reconfigurable equalization circuit. In the analysis process, we need to use the battery model, we use the Thevenin equivalent circuit model because it is simple and can better reflect the real situation of the battery, the Thevenin equivalent circuit model is shown in Fig. 4. Where UOCV denote OCV, which has a corresponding functional relationship with SOC
OCV = f (SOC )
dUp Up + =I dt Rp
3.1. Starting equilibrium Suppose that the voltage of cell B1 is the highest while cell Bn is the lowest in the battery pack, cell Bn will be isolated from the battery pack when the voltage difference between cell B1 and cell Bn is as
U 1 − Un ≥ Uset
(8)
Where U1 and Un are the voltages of cell B1 and cell Bn, respectively, Uset is the equalization threshold voltage. Since the states of cell B1 and cell Bn are the same before equalization, the polarization voltage is also the same, refer to (5), (8) is rewritten as
(4)
As shown in Fig. 4, R is the ohmic resistance, Rp and Cp are polarization resistance and polarization capacitance, respectively, and the terminal voltage U is given by
UOCV 1 − UOCVn ≥ Uset + ΔRI
U = UOCV − IR − Up
Where UOCV1 and UOCVn are the OCV of cell B1 and cell Bn, respectively,
(5)
Fig. 4. Thevenin equivalent circuit model. 3
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Fig. 5. The ΔSOC while balancing if ΔR = 0.
ΔR is the ohmic resistance difference between cell B1 and cell Bn. Usually, Uset is constant, if ΔR = 0, the difference between the SOC of two cells (ΔSOC) while balancing as shown in Fig. 5. C is the relationship between SOC and OCV (refer to (4)), as shown in Fig. 5, because the SOC of cell has a strong nonlinear relationship with OCV, even if the difference between OCVs of two cells is the same (Uset), their SOC difference will be different (ΔSOC1 > ΔSOC2). As shown in Fig. 6, suppose that the SOC of cell B1 is higher than cell Bn, that is, UOCV1 ＞ UOCVn. However, if the ohmic resistance of the cell B1 is higher than that of cell Bn(yellow area), and the other parameters and states of the two cells are the same(green area), the terminal voltage of the cell Bn may be higher than the terminal voltage of the cell B1(red area), which may cause the system to consider the SOC of cell Bn is lower than cell B1. Refer to (4) and (9), and the analysis above, whether cell Bn will be isolated from the battery pack is not only related to the SOC difference between cell B1 and cell Bn, but also largely due to the difference in cell ohmic resistance, current and SOC, which is very unreasonable.
3.2. Ending equilibrium Cell Bn will return to the initial state when the difference between the voltages of cell B1 and cell Bn as
U 1 − Un ≤ 0
(10)
However, cell Bn is isolated from the battery pack and cell B1 supplies power to the load, refer to (5), the voltages of cell B1 and cell Bn can be written as (11) and (12), respectively, as shown in Fig. 7.
U 1 = UOCV 1 − IR1 − Up1
(11)
Un = UOCVn − Upn
(12)
As shown in Fig. 7, although the terminal voltages of cell B1 and cell B2 are the same (red area), however, the status of cell B1 and cell B2 is different (cell B1 is discharging and cell Bn is resting), making their ohmic voltage and polarization voltage different(red area and green area),that is, UOCV1≠UOCVn, and SOC1≠SOCn. The difference between the voltages of cell B1 and cell Bn is given
Fig. 6. Refer to Fig. 4, the voltage of cell B1and cell Bn while discharging.
Fig. 7. The voltage of cell B1 and cell Bn while cell Bn is balanced. 4
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by
U 1 − Un = (UOCV 1 − UOCVn) − IR1 − (Up1 − Upn)
(13)
Refer to (7), when cell Bn is not isolated from the battery pack, the initial polarization voltages of cell B1 and cell Bn are the same. However, when cell Bn is isolated from the battery pack, its current is 0 but cell B1 is not. The relationship between the polarization voltage and the terminal voltage of cell B1and cell Bn is given by (14) and (15), respectively.
Up1 − Upn > 0
(14)
U 1 − Un < UOCV 1 − UOCVn
(15)
Refer to (15), the difference between the voltages of cell B1 and cell Bn is always less than the difference between OCV, which is the difference between SOC. While the voltage balancing control scheme is used and it is considered that cell Bn has been equalized, in fact, cell Bn and cell B1 do not reach a true consistency. Fig. 8. The error of G.
4. Voltage-SOC balancing control scheme
G (SOCave ) =
4.1. Principle of voltage-SOC balancing control scheme
1 f ′ (SOCave )
(25)
We rewrite (23) as
In this section, we introduce the principle of the voltage-SOC balancing control scheme, and compare it with the voltage balancing control scheme and the SOC balancing control scheme, suppose that the SOC of cell B1 is the highest and cell Bn is the lowest in the battery pack, refer to (4), obtained by lagrange mean value theorem.
ΔSOC = G (SOCave ) × ΔOCV
(26)
ΔOCV = f (SOC1) − f (SOCn)
(18)
The error of ΔSOC is proportional to G. Since the cell parameters in the battery pack obey the normal distribution [31], SOCave is approximately the SOC average of all the cells. Suppose that the SOC of each cell in the battery pack be within [SOCi, SOCi+1], and G is an increasing function, the error of G is shown in Fig. 8. G(SOCζ) and G(SOCave) are between G(SOCi) and G(SOCi+1), usually, G(SOCζ)≠G(SOCave), as shown in Fig. 8. If SOCζ = SOCi, errmax is given by
ΔSOC = SOC1 − SOCn
(19)
err max =
(20)
While ΔSOC is known, because of the Ah integral method is simple, the time of ending the equilibrium can be determined by the Ah integral method, Ah integral method is as follows:
(21)
ΔSOC =
f (SOC1) − f (SOC1) = f ′ (SOCξ ) × (SOC1 − SOCn)
(16)
SOCn < SOCξ < SOC1
(17)
ΔOCV and ΔSOC are defined as
we rewrite (16) as
ΔOCV = f ′ (SOCξ ) × SOCn The SOC of the battery pack SOCave is known, if
SOC1 − SOCn → 0 The following equation can be obtained
SOCξ = SOCave
ΔOCV f ′ (SOCave )
(23)
Refer to (23), while ΔOCV and f’(SOCave) are known, the difference in SOC between any cells can be estimated indirectly. Before cell Bn is isolated from the battery pack, cell B1 and cell Bn are in the same state, and their polarization voltages are the same, ΔOCV is given by
ΔOCV = U 1 − Un − ΔRI
1 Q
∫0
T
ηIdt
(27)
(28)
Where I is the absolute value of the current amplitude at each moment, refer to (2), and the analysis in part 2, if ΔSOC=ΔSOCB1n, the SOCs of cell B1 and cell Bn are the same. That is to say, after the cell Bn is isolated from the battery pack, if the SOC of the cell B1 drops is equal to the ΔSOC, the equalization can be considered complete. The voltage-SOC balancing control scheme proposed in this paper cannot estimate the SOC of each cell, it can estimate the difference between the SOC of the two cells. When we know the difference between the SOC of the two cells, we know which cell need to be balanced, we can know the moment when their SOC reaches the same through Ah-counting. Therefore, the method proposed in this paper can better balance the battery pack without knowing the SOC of cell. However, it must be noted that the Ah-counting method that in principle is open-loop, will inevitably be affected by measurement noise and other factors. In general, the SOC obtained by the Ah-counting is not equal to the SOC estimated by the proposed method, leading to overbalance or underbalance. If the error is small, this overbalance or underbalance is allowed, because the battery pack allows for some inconsistency. However, if the error is large, this equilibrium will likely have little effect or negative effect (if the error is greater than 100%), but this will eventually be detected by the system because its true SOC change does not reach the expected result. When the equalization is over, the system will operate again until the cell reaches the operating conditions.
(22)
We rewrite (20) as
ΔSOC =
G (SOCave ) − G (SOCi) G (SOCi)
(24)
Refer to (23) and (24), the relationship between OCV and SOC, the SOC of battery pack are known, and the terminal voltage and current of the cell are easily obtained, so that the ΔSOC can be easily obtained by the difference in the terminal voltage of the cell. However, refer to (21), the error estimated by voltage-SOC control scheme has a great relationship with the consistency of the battery pack, if the SOC of the cell in the battery pack is almost uniform, the error is small. However, the SOC difference of the cell is always present, which causes an error in the ΔSOC. The following is an analysis of the error of ΔSOC. G(SOCave) is defined as 5
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Fig. 9. The equalization process of voltage balancing control scheme, SOC balancing control scheme and voltage-SOC balancing control scheme.
4.2. Comparison and analysis with voltage balancing control scheme and SOC balancing control scheme The equalization process of voltage balancing control scheme, SOC balancing control scheme and voltage-SOC balancing control scheme is shown in Fig. 9. As shown in Fig. 9, the voltage balancing control scheme and SOC balancing control scheme respectively calculate the difference between the voltage and SOC of cells, and thereby achieving the goal of battery pack equalization. The voltage-SOC equalization method first calculates the difference between the voltages of cells, and then the SOC difference of the cell is estimated through G. Finally, the difference between the SOC of the cell is used to achieve equalization like the voltage balancing control scheme, realizing the conversion from the voltage balancing control scheme to the SOC balancing control scheme. It does not have the disadvantage that the SOC of each cell is difficult to obtain, and the parameter (voltage) is greatly affected by the state of cell. As shown in Table 1, compared with the voltage balancing control scheme, the voltage-SOC balancing control scheme only adds the calculation of G, but gets rid of the defect that the parameter of the voltage balancing control scheme is easily affected by the state of cell. Compared with the SOC balancing control scheme, the voltage-SOC balancing control scheme can obtain the difference of SOC without complex SOC estimation of cell, which has the advantages of SOC balancing control scheme to a certain extent.
Fig. 10. SOC-OCV curve. Table 2 Ohmic resistance of 5 cells.
Ohmic resistance/mΩ
Cell 1
Cell 2
Cell 3
Cell 4
Cell 5
80
80
85
70
68
Table 3 Initial voltage of 5 cells.
5. Experience 5.1. Experimental preparation
Voltage/mV
This paper chooses 18,650 lithium-ion battery produced by SAMSUNG for the experiment, whose nominal capacity and voltage are 2.2 Ah and 3.7 V, respectively. The SOC-OCV curve is shown in Fig. 10. we rewrite (4) as (29).
OCV = 14.406 × SOC5 − 43.594 × SOC 4 + 49.241 × SOC 3 − 24.926 × SOC 2 + 6.0253 × SOC + 3.0008
Cell 1
Cell 2
Cell 3
Cell 4
Cell 5
4134
4116
4135
4140
4136
The ohmic resistance of the cell changes little from 0 to 100% [21], and the ohmic resistance of each cell is replaced by the average value of the ohmic resistor. The ohmic resistance and initial voltage of the cell used in the experiment are shown in Tables 2 and 3, respectively. The MCU used in the experiment is STM32F407. To measure the
(29)
Table 1 Advantages and disadvantages of voltage balancing control scheme, SOC balancing control scheme and voltage-SOC balancing control scheme. Advantages
Disadvantages
Voltage balancing control scheme
Simple, because the voltage of each cell is easy to obtain
SOC balancing control scheme
The parameter (SOC) is less affected by the statue of cell
Voltage-SOC balancing control scheme
Simple, it is easy to obtain the difference in SOC of two cells indirectly, and the parameter (SOC) is less affected by the statue of cell
The parameter (voltage) is greatly affected by the state of cell Complex, because the SOC of each cell is not easy to obtain The estimated accuracy of the difference in SOC largely dependent on G
6
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Fig. 11. Equilibrium experiment platform.
Fig. 12. The voltage of cell 2 and cell 4.
voltage of the cell, the LTC6804 manufactured by Linear technology is used. This chip is powerful and can measure the voltage of 12 seriesconnected cells, the maximum error is 1.2 mV. A 3Ω sampling resistor is used to measure the current. The load is replaced by a 100Ω sliding rheostat. Since it is not necessary to estimate the SOC of the cell for a long time, the SOC of each cell is estimated by the Ah integral method and is regarded as the SOC true value. The voltage, SOC and current are displayed on 3.2-inch TFT color screen. The equilibrium experimental platform is shown in Fig. 11.
balancing control scheme is not satisfactory, whether at the beginning of equilibrium or at the end of equilibrium. This is because the voltage of the cell is easily affected by the state of the cell.
5.3. Verification of the performance of voltage-SOC balancing control scheme We use the voltage - SOC balancing control scheme experiment again. While ΔSOC > 1%, the cell with the lowest SOC will be isolated from the battery pack. In the experiment, 0–30 s, the battery pack is in no-load state, the difference between the terminal voltage is equal to the difference of the OCV. After 30 s, the battery pack is connected to the sliding rheostat. The voltage of 5 cells are shown in Fig. 13. As shown in Fig. 13, at 360 s, cell 2 has been equalized, and the voltage of cell 2 gradually approaches the battery pack, achieving the equilibrium goal that the voltage balancing control scheme hopes to achieve. The difference is that it has no disadvantages of the voltage balancing control scheme (as shown in Fig. 12), also, we did not achieve the above goal by estimating the SOC of all the cells, but by measuring the terminal voltage. However, the difference in voltages of cell 1, cell 3, cell 4, cell 5 is significantly increased after 30 s compared with 0 s, the initial voltage difference between cell 3 and cell 4 is 5 mV, but at 180 s, it rises to 11 mV, mainly because the ohmic resistance of cell 3 and cell 4 are different, as shown in Table 2, the ohmic resistance of cell 3 is 85mΩ, and the cell 4 is 70mΩ, cell 3 and cell 4 have different ohmic voltage drops, which makes their voltage difference. The SOC of 5 cells are as shown in Fig. 14. As shown in Fig. 14, at 360 s, the SOCs of cell 2 and cell 4 are almost
5.2. Verification of the shortcomings of voltage balancing control scheme Refer to (9), suppose that Uset = 20 mV, ΔR = 0, the SOC of cell B1 is the highest and cell Bn is the lowest in the battery pack, ΔSOC1n is defined as (30)
ΔSOC1n = ΔSOCB1 − ΔSOCBn
Refer to (29), if SOCB1 = 90%, SOCB1 = 50% and SOCB1 = 30% respectively, SOCBn and ΔSOC1n when the cell Bn will be isolated from the battery pack are shown in Table 4. As shown in Table 4, if SOCB1 = 90%, while ΔSOC1n = 2.14%, the cell Bn will be isolated from the battery pack, but when SOCB1 = 30%, ΔSOC1n will rise to 5.09%, which is about 2.38 times that of 90%. This is very unreasonable. We experimented with voltage balancing control scheme with Uset = 20 mV. Fig.12 shows the voltage of cell 2 and cell 4. To facilitate the recording of data, the equalization system refreshes every 10 s. 0 s: The voltage difference between cell 2 and cell 4 is about 24 mV, cell 2 satisfies the equalization condition, and cell 2 will be isolated from the battery pack. 10 s: Cell 2 is isolated from the battery pack and its voltage remains constant, while cell 4 supplies the load with a voltage drop of about 28 mV, so that the voltage of cell 2 is higher than cell 4. At this point, the equalization system will assume that cell 2 has been equalized. 20 s: Cell 2 supplies power to the load. However, the change of cell 2 status makes its voltage jump correspondingly. As a result, the voltage of cell 2 is still lower than that of cell 4. As shown in Table 4 and Fig. 12, the performance of the voltage Table 4 SOCBn and ΔSOC1n while SOCB1 = 90%, SOCB1 = 50% and SOCB1 = 30% respectively. SOCB1/%
SOCBn/%
ΔSOC1n/%
90 50 30
87.86 45.86 24.91
2.14 4.14 5.09
Fig. 13. The voltage of 5 cells. 7
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Fig. 17. About 30% of the battery pack, the SOC of 5 cells.
Fig. 14. The SOC of 5 cells.
Table 5 The comparison of Figs. 14–17.
U24/mV ΔOCV24/mV G/mV/% ΔSOC24c/% ΔSOC24r/% ΔSOCe/% error/%
Fig. 14
Fig. 15
Fig. 16
Fig. 17
24 24 0.071 1.704 1.7 0.004 0.24
22.3 16.1 0.1121 1.8 1.71 0.09 5.3
19.5 13.9 0.123 1.71 1.8 −0.09 −5
7.8 3.6 0.42 1.512 1.5 0.012 0.8
Fig. 15. About 83% of the battery pack, the SOC of 5 cells.
Fig. 18. ΔSOCe and error.
Fig. 16. About 53% of the battery pack, the SOC of 5 cells.
the same, which proves that the voltage-SOC balancing control scheme performs well. In order to further verify the performance of the voltageSOC balancing control scheme, about 83%, 53% and 30% of the battery pack are tested respectively. In the experiment, the equalization system is activated at a certain time, and cell 2 is balanced. In other words, before the equalization system is not enabled, the battery pack can be considered as having no equalization system. The difference between the OCV and the ΔSOC is not calculated. The time for the balanced system to work is 0 s, the SOC of each cell are shown in Figs. 15–17. As shown in Figs. 14–17, about 360 s, 420 s, 420 s and 410 s, respectively, cell 2 have been equalized, and the voltage-SOC balancing
Fig. 19. The maximum error of G.
8
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refer to (27), but usually such cases will not occur, so the error generated by G, which is the error of the estimated difference of SOC, will be reduced correspondingly. Moreover, if the SOC difference between cell B1 and cell B2 is 1%, even if the error of G reaches a maximum of 9%, the method proposed in this paper estimates that the SOC difference between these two cells is 1.09%, and the impact of the error is small. 6. Conclusion Due to the inconsistent state of the cell, the voltage balancing control scheme has great limitations when applied to the reconfigurable equalization circuit, for other equalization circuits, the voltage balancing control scheme also has limitations. This paper proposes a voltageSOC balancing control scheme, which only needs the difference between the terminal voltage and the SOC of battery pack, and can get the difference between the SOC of any cell, it is simple and has excellent performance, and the experimental results prove it. By using the proposed control scheme, it is possible to provide a simple, easy-to-acquire, accurate equalization parameter for the BMS (battery management system). In the future work, we will further consider the differences in the SOH (state of health) of each cell in the battery pack and the differences in the OCV-SOC curve of the cell to reduce the estimation errors caused by the voltage-SOC balancing control scheme.
Fig. 20. The maximum error of G (LFP batteries).
control scheme has better completed the task of balancing the battery pack. Then we will analyze the error of the voltage-SOC balancing control scheme. U24, ΔOCV24, ΔSOC24c, ΔSOC24r and ΔSOCe are defined as
U 24 = U 2 − U 4 ⎧ ⎪ ΔOCV 24 = U 24 − I (R2 − R 4) ⎨ ΔSOC 24c = G × ΔOCV 24 ⎪ ΔSOC 24r = SOC 2 − SOC 4 ⎩ ΔSOCe = ΔSOC 24c − ΔSOC 24r
Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No. 51677058).
(31)
Where U2, U4, R2, R4, SOC2 and SOC4 are the voltage, ohmic resistance and SOC of cell 2 and cell 4, respectively. The comparison of Figs. 14–17 are shown in Table 5. ΔSOCe and error are shown in Fig. 18. As shown in Table 5, the voltage-SOC balancing control scheme is used to estimate the difference of ΔOCV24 between cell 2 and cell 4 by ohmic resistance, voltage and current, respectively 24 mV, 16.1 mV, 13.9 mV and 3.6 mV. Of course, this is not accurate because the LTC6804 and the sampling resistor are erroneous, and we don't know the value of the ohmic resistance of each cell. According to the SOC of the battery pack, G is 0.071, 0.1121, 0.123 and 0.42, respectively, ΔSOC24c are 1.704%, 1.8%, 1.71% and 1.512%, compared with 1.7%, 1.71%, 1.8% and 1.5%, as shown in Fig. 18, the maximum error appears in Fig. 15, about 5.3%, which is equivalent to the equilibrium performance of the SOC balancing control scheme with the SOC estimation error within 5%. Although the voltage-SOC balancing control scheme performs well, there are still errors. Refer to (23), the error of the voltage-SOC balancing control scheme mainly comes from two aspects. One is the error caused by ΔOCV24, including voltage, current, and internal resistance of the cell. The second is the error caused by G. Since (21) is not satisfied, the error of ΔSOC24c estimated by (23) is shown in (27). If ΔSOC is 1%, we calculate with the data of (29) in the case of Fig. 7 and (27), the maximum error of the G is shown in Fig. 19. As shown in Fig. 19, the maximum error of G appears in about 20%, and the maximum error is about 7%, but most of it can be kept within 4%, so that the theoretical error of the voltage-SOC balancing control scheme is hardly more than 4%. We use LiFePO4 (LFP) batteries produced by LISHENG to calculate the maximum error of G, as shown in Fig. 20, the maximum error of G occurs at about 20%, and the maximum error is about to 9%, but most of it can be kept within 5%. The maximum error of G in Fig. 20 is obviously higher than that in Fig. 19, this is because the OCV-SOC curve of the LFP batteries is flat in a wide SOC range compared with experimental batteries. However, please note that in both Figs. 19 and 20, extreme cases are considered,
References [1] F. Ju, W. Deng, J. Li, Performance evaluation of modularized global equalization system for lithium-ion battery packs, IEEE Trans. Autom. Sci. Eng. 13 (April (2)) (2016) 986–996. [2] K.M. Lee, S.W. Lee, Y.G. Choi, et al., Active balancing of Li-Ion battery cells using transformer as energy carrier, IEEE Trans. Ind. Electron. 64 (February (2)) (2017) 1251–1257. [3] J. Wei, G. Dong, Z. Chen, System state estimation and optimal energy control framework for multicell lithium-ion battery system, Appl. Energy 187 (February (1)) (2017) 37–49. [4] Y. Chen, X. Liu, Y. Cui, et al., A multiwinding transformer cell-to-cell active equalization method for lithium-ion batteries with reduced number of driving circuits, IEEE Trans. Power Electron. 31 (July (7)) (2016) 4916–4929. [5] M.Y. Kim, C.H. Kim, J.H. Kim, et al., A chain structure of switched capacitor for improved cell balancing speed of lithium-ion batteries, IEEE Trans. Ind. Electron. 61 (August (8)) (2014) 3989–3999. [6] G. Gunlu, Dynamically reconfigurable independent cellular switching circuits for managing battery modules, IEEE Trans. Energy Convers. 32 (March (1)) (2016) 194–201. [7] L. He, Z. Yang, Y. Gu, et al., SoH-aware reconfiguration in battery packs, IEEE Trans. Smart Grid 9 (July (4)) (2018) 3727–3735. [8] T. Morstyn, M. Momayyezan, B. Hredzak, et al., Distributed control for state-ofcharge balancing between the modules of a reconfigurable battery energy storage system, IEEE Trans. Power Electron. 31 (November (11)) (2016) 7986–7995. [9] X. Cui, W. Shen, Y. Zhang, et al., Novel active LiFePO4 battery balancing method based on chargeable and dischargeable capacity, Comput. Chem. Eng. 97 (February (1)) (2017) 27–35. [10] C. Song, N. Lin, D. Wu, Reconfigurable battery techniques and systems: a survey, IEEE Access 4 (March (1)) (2016) 1175–1189. [11] F. Baronti, R. Roncella, R. Saletti, Performance comparison of active balancing techniques for lithium-ion batteries, J. Power Sources 267 (December (4)) (2014) 603–609. [12] D.D. Quinn, T.T. Hartley, Design of novel charge balancing networks in battery packs, J. Power Sources 240 (October (1)) (2013) 26–32. [13] L. Zhong, C. Zhang, Y. He, et al., A method for the estimation of the battery pack state of charge based on in-pack cells uniformity analysis, Appl. Energy 113 (January (1)) (2014) 558–564. [14] J. Meng, M. Ricco, G. Luo, et al., An overview and comparison of online implementable SOC estimation methods for lithium-ion battery, IEEE Trans. Ind. Appl. 54 (March (2)) (2018) 1583–1591. [15] S. Nejad, D.T. Gladwin, D.A. Stone, A systematic review of lumped-parameter equivalent circuit models for real-time estimation of lithium-ion battery states, J. Power Sources 316 (June (1)) (2016) 183–196.
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[24] L. Zheng, J. Zhu, G. Wang, et al., Model predictive control based balancing strategy for series-connected lithium-ion battery packs, 2017 19th European Conference on Power Electronics and Applications (EPE’17 ECCE Europe) (2017). [25] X. Tang, C. Zou, T. Wik, et al., Run-to-run control for active balancing of lithium iron phosphate battery packs, IEEE Trans. Power Electron. (May) (2019). [26] N. Bouchhima, M. Gossen, S. Schulte, et al., Life-time of self-reconfigurable batteries compared with conventional batteries, J. Energy Storage 15 (February (1)) (2018) 400–407. [27] Y. Wang, C. Zhang, Z. Chen, et al., A novel active equalization method for lithiumion batteries in electric vehicles, Appl. Energy 145 (May (1)) (2015) 36–42. [28] W. Huang, J.A.A. Qahouq, Energy sharing control scheme for state-of-charge balancing of distributed battery energy storage system, IEEE Trans. Ind. Electron. 62 (May (5)) (2015) 2764–2776. [29] T.H. Phung, J. Crebier, A. Chureau, et al., Optimized structure for next-to-next balancing of series-connected lithium-ion cells, IEEE Trans. Power Electron. 29 (September (9)) (2013) 4603–4613. [30] Y. Xiangwu, G. Qi, Y. Yang, et al., Study on methods for estimating the state of health of battery pack, J. Hunan Univ. 42 (February (2)) (2015) 93–99. [31] T. Baumhöfer, M. Brühl, S. Rothgang, et al., Production caused variation in capacity aging trend and correlation toinitial cell performance, J. Power Sources 247 (February (3)) (2014) 332–338.
[16] S.C. Choi, J.Y. Jeon, T.J. Yeo, et al., State-of-charge balancing control of a battery power module for a modularized battery for electric vehicle, J. Electr. Eng. Technol. 11 (November (3)) (2016) 629–638. [17] M.A. Hannan, M.M. Hoque, S.E. Peng, et al., Lithium-ion battery charge equalization algorithm for electric vehicle applications, IEEE Trans. Ind. Appl. 53 (May (3)) (2017) 2541–2549. [18] B. Dong, Y. Li, Y. Han, Parallel architecture for battery charge equalization, IEEE Trans. Power Electron. 30 (September (9)) (2017) 4906–4913. [19] Y. Shang, C. Zhang, N. Cui, et al., A cell-to-Cell battery equalizer with zero-current switching and zero-voltage gap based on quasi-resonant LC converter and boost converter, IEEE Trans. Power Electron. 30 (July (7)) (2015) 3731–3747. [20] D. Kim, J. Lee, Discharge scheduling for voltage balancing control scheme in reconfigurable battery systems, Electron. Lett. 53 (March (7)) (2017) 496–498. [21] L. He, L. Kong, S. Lin, et al., RAC: reconfiguration-assisted charging in large-scale lithium-ion battery systems, IEEE Trans. Smart Grid 7 (May (3)) (2016) 1420–1429. [22] W. Feng, L. Cheng, J. Jiuchun, et al., A New evaluation method to the consistency of lithium-ion batteries in electric vehicles, Asia-Pacific Power and Energy Engineering Conference (2012). [23] H. Weiji, Z. Changfu, Z. Chen, et al., Estimation of cell SOC evolution and system performance in module-based battery charge equalization systems, IEEE Trans. Smart Grid (Aug) (2018).
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Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Voltage-SOC balancing control scheme for series-connected lithium-ion battery packs
T
⁎
Tiezhou Wu, Feng Ji , Li Liao, Chun Chang Hubei Key Laboratory for High-efficiency Utilization of Solar Energy and Operation Control of Energy Storage System, Hubei University of Technology, Hubei, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Voltage balancing control scheme SOC balancing control scheme Reconfigurable equalization circuit Cell
The basis for determining whether the cell needs to be balanced is generally the voltage or SOC (state of charge), the voltage balancing control scheme is simple but performs poorly, the SOC balancing control scheme performs well but needs to estimate the SOC of all cells. Based on the analysis why existing naive approaches are not effective for voltage balancing control scheme, the voltage-SOC balancing control scheme is proposed, which has the advantages of simple of voltage balancing control scheme and well performance of SOC balancing control scheme. By utilizing the difference of voltage of cell and SOC of battery pack, the difference of SOC between two cells can be obtained indirectly, and the transition from voltage balancing control scheme to SOC balancing control scheme can be realized, while the advantages of voltage balancing control scheme and SOC balancing control scheme are retained. The 4 experiments designed show that the estimated errors of the difference between the SOCs of the two cells are 0.24%, 5.3%, -5%, and 0.8%, respectively, which proves the excellent performance of voltage-SOC balancing control scheme.
1. Introduction Lithium-ion batteries are widely used in a variety of applications, including electric vehicles, energy storage systems, due to their high energy density, long cycle life and low self-discharge rate [1]. A number of battery cells are usually connected in series in order to supply higher voltage and higher power to the load in a wide range of applications, while significant efforts are made by designers to select the battery cells such that they are as identical/matched as possible, the battery cells will still have mismatches in practice due to manufacturing tolerances, different self-discharge rates, uneven operating temperature across the battery cells, and nonuniform aging process, among others. Such inevitable differences within battery cells will drift apart through cycling and could potentially lead to overcharging or over discharging, It is clear that such non-uniformity limits the battery capacity and may even cause safety issues. Therefore, to properly maintain all cells balanced is of significant importance for enhancing battery life [2–5]. Mounting research efforts have been devoted to investigating efficient cell equalizers, attentions have been also focused on the control scheme and topological structure of equalization system (see reviews [6–9]), advantages and disadvantages of various types of cell equalizers are summarized in [10,11]. The basis for determining whether the cell needs to be balanced is generally the voltage or SOC, the voltage of cell
⁎
is relatively easy to obtain, but it is greatly affected by factors such as working conditions, making it difficult to provide accurate parameters for the equalization system [12]. SOC balancing control scheme is less affected by the working state of the cell, and its equalization performance is related to the accuracy of SOC estimation [13]. In order to obtain accurate SOC of cell, it is often necessary to use complex algorithm to estimate the SOC of each cell in the battery pack, which makes the SOC balancing control scheme has disadvantages such as large amount of calculation and complexity, the SOC estimation algorithm are discussed in [14,15]. To verify the performance of the proposed equalization circuit or equalization method, most papers use the SOC balancing control scheme, however, they often ignore complex SOC estimates and consider the SOC of each cell to be known and accurate [16–19]. But in practice, the shortcomings of the SOC balancing control scheme cannot be ignored. A lot of work has been done on the shortcomings of the voltage balancing control scheme and the SOC balancing control scheme. Kim et al. used the terminal voltage to estimate the SOC by establishing a battery model [20]. He et al. and Feng et al. improve the performance of voltage balancing control scheme by increasing the OCV (open circuit voltage), polarization voltage, capacity, and other parameters [21,22]. In addition, Han et al. develop computationally efficient methods to estimate the battery cell SOC [23]. Model predictive control methods have shown better performance but require
Corresponding author. E-mail address: [email protected] (F. Ji).
https://doi.org/10.1016/j.est.2019.100895 Received 25 June 2019; Received in revised form 8 August 2019; Accepted 8 August 2019 Available online 20 August 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
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massive computational resources and time [24]. The run-to-run control method proposed by Tang et al. is easy to implement and has good performance [25]. In this paper, a voltage-SOC balancing control scheme is proposed, which can indirectly estimate the difference between the SOCs of the cell through the terminal voltage and the SOC of battery pack. It combines the advantages of simple and better performance, and also avoids the disadvantage of large amount of calculation of SOC balancing control scheme and poor performance of voltage balancing control scheme. This paper provides three contributions. 1) First, based on the reconfigurable equalization circuit, why the voltage balancing control scheme provides the error parameters for the equalization system is further analyzed. 2) Second, a voltage-SOC balancing control scheme is proposed and compared with the voltage balancing control scheme and the SOC balancing control scheme. 3) Third, the performance of the voltage-SOC balancing control scheme is verified by extensive experiment results. 2. Reconfigurable equalization circuit Compared with the traditional equalization circuit, the reconfigurable equalization circuit has the advantages of high balanced conversion efficiency and can extend the life of the battery pack [26]. Based on the reconfigurable equalization circuit, this paper analyzes the shortcomings of the voltage balancing control scheme and verifies the superiority of the voltage-SOC balancing control scheme. In this section, we use SOC balancing control scheme to briefly introduce the working principle of reconfigurable equalization circuit. The detailed introduction of reconfigurable equalization circuit can be referred to [27–29]. As shown in Fig. 1, for the cell Bn, its discharge (charge) state is controlled by the switches Sn1 and Sn2. For example, while Sn1 is ON and Sn2 is OFF, cell Bn is in a discharging (charging) state, and while Sn1 is OFF and Sn2 is ON, cell Bn is isolated from the battery pack.
Fig. 2. Cell Bn is isolated from the battery pack when the pack is discharged.
At T1, suppose that the SOC of cell Bn is lower and the SOC of cell B1 is higher, the difference between the SOCs of the two cells is given by (1)
ΔSOCT 1 = SOCB1 − SOCBn
Where SOCB1 and SOCBn are the SOCs of cell B1 and cell Bn, respectively. To make the SOC of cell Bn and cell B1 the same, that is, ΔSOCT1 = 0, when the pack is discharged, let Sn1 OFF and Sn2 ON, as shown in Fig. 2. As shown in Fig. 2, cell Bn is isolated from the battery pack, but the remaining cells are powering the load. If the current of the pack during T1-T5 is shown in Fig. 3, where the current is positive for charging and negative for discharging, I1, I2, I3 and I4 are the current of T1-T2, T2-T2, T3-T4 and T4-T5, respectively. T1-T2: Cell Bn is isolated from the pack (as shown in Fig. 2), and its SOC remains unchanged, but cell B1 is discharging, its SOC will decline, and the SOC of cell Bn is closer to that of cell B1 (assuming that the SOC of cell B1 is still higher than that of cell Bn at T2). T2-T3: Since the current is 0, the difference between the SOCs of the two cells does not change. T3-T4: The pack is charged, and cell Bn will be connected to the battery pack. Just like cell B1, its SOC will increase, and the difference between the SOCs of the two cells does not change. T4-T5: The pack is discharged, and cell Bn will be isolated from the pack, similar to TI-T2. Then, during T1-T5, the SOC of cell B1 is decreased by ΔSOCB1n more than the cell Bn.
ΔSOCB1n = −
1 ( QB1
T2
∫T1
ηI 1dt+
T3
∫T 2
ηI 2dt+
T4
∫T 3
0dt+
T5
∫T 4
ηI 4dt ) (2)
Where QB1 is the capacity of the cell B1, η is the coulombic efficiency. Refer to (2), the current during T3-T4 is 0, because during charging, cell Bn will be connected to the battery pack without isolation, so at T5, the difference in SOC between cell B1 and cell Bn is given by
ΔSOCT 5 = ΔSOCT 1 − ΔSOCB1n
Fig. 1. Reconfigurable equalization circuit. 2
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Fig. 3. The current of the pack during T1-T5.
If ΔSOCT5 = 0, the equalization system has completed the equalization task for the cell Bn. If the current during T1-A is large enough that the SOC of cell B1 decreases is equal to the SOC difference between cell B1 and cell Bn, cell Bn will be connected to the battery pack because their SOC is the same. Through the above analysis, it can be known that when the battery pack is discharged, the circuit will isolate the cell with a lower SOC. Similarly, when the battery pack is charged, the circuit can also improve the consistency of the battery pack by isolating the cell with a higher SOC. The current direction could change significantly with time in many battery applications, so that the cell that is isolated during discharge needs to be connected to the battery pack if the current direction changes, although it is not well balanced, as shown in Fig. 3, the equalization can be completed after multiple equalization.
Where Up is the polarization voltage, can be calculated as
Cp
(6)
Refer to (5) and (6), Up is given by t
t
Up (t ) = Up (0) e− R1C1 + IR1(1 − e− R1C1 )
(7)
Refer to (5) and (7), the terminal voltage U is not only related to the SOC of the cell (refer to (4)), but also related to such as current I, ohmic resistance R, the state of cell (such as discharging, resting), so that the terminal voltage U does not reflect the SOC of the cell well. Considering that the inconsistency of the cell parameters is mainly due to the difference in the using process, the difference in polarization voltage drop is much smaller than the difference in ohmic voltage drop of the cell [30]. For simplicity and clarity, it is considered that the cells in the battery pack have the same polarization voltage under the same working conditions.
3. Disadvantages of voltage balancing control scheme In this section, we will analyze the shortcomings of the voltage balancing control scheme applied to the reconfigurable equalization circuit. In the analysis process, we need to use the battery model, we use the Thevenin equivalent circuit model because it is simple and can better reflect the real situation of the battery, the Thevenin equivalent circuit model is shown in Fig. 4. Where UOCV denote OCV, which has a corresponding functional relationship with SOC
OCV = f (SOC )
dUp Up + =I dt Rp
3.1. Starting equilibrium Suppose that the voltage of cell B1 is the highest while cell Bn is the lowest in the battery pack, cell Bn will be isolated from the battery pack when the voltage difference between cell B1 and cell Bn is as
U 1 − Un ≥ Uset
(8)
Where U1 and Un are the voltages of cell B1 and cell Bn, respectively, Uset is the equalization threshold voltage. Since the states of cell B1 and cell Bn are the same before equalization, the polarization voltage is also the same, refer to (5), (8) is rewritten as
(4)
As shown in Fig. 4, R is the ohmic resistance, Rp and Cp are polarization resistance and polarization capacitance, respectively, and the terminal voltage U is given by
UOCV 1 − UOCVn ≥ Uset + ΔRI
U = UOCV − IR − Up
Where UOCV1 and UOCVn are the OCV of cell B1 and cell Bn, respectively,
(5)
Fig. 4. Thevenin equivalent circuit model. 3
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Fig. 5. The ΔSOC while balancing if ΔR = 0.
ΔR is the ohmic resistance difference between cell B1 and cell Bn. Usually, Uset is constant, if ΔR = 0, the difference between the SOC of two cells (ΔSOC) while balancing as shown in Fig. 5. C is the relationship between SOC and OCV (refer to (4)), as shown in Fig. 5, because the SOC of cell has a strong nonlinear relationship with OCV, even if the difference between OCVs of two cells is the same (Uset), their SOC difference will be different (ΔSOC1 > ΔSOC2). As shown in Fig. 6, suppose that the SOC of cell B1 is higher than cell Bn, that is, UOCV1 ＞ UOCVn. However, if the ohmic resistance of the cell B1 is higher than that of cell Bn(yellow area), and the other parameters and states of the two cells are the same(green area), the terminal voltage of the cell Bn may be higher than the terminal voltage of the cell B1(red area), which may cause the system to consider the SOC of cell Bn is lower than cell B1. Refer to (4) and (9), and the analysis above, whether cell Bn will be isolated from the battery pack is not only related to the SOC difference between cell B1 and cell Bn, but also largely due to the difference in cell ohmic resistance, current and SOC, which is very unreasonable.
3.2. Ending equilibrium Cell Bn will return to the initial state when the difference between the voltages of cell B1 and cell Bn as
U 1 − Un ≤ 0
(10)
However, cell Bn is isolated from the battery pack and cell B1 supplies power to the load, refer to (5), the voltages of cell B1 and cell Bn can be written as (11) and (12), respectively, as shown in Fig. 7.
U 1 = UOCV 1 − IR1 − Up1
(11)
Un = UOCVn − Upn
(12)
As shown in Fig. 7, although the terminal voltages of cell B1 and cell B2 are the same (red area), however, the status of cell B1 and cell B2 is different (cell B1 is discharging and cell Bn is resting), making their ohmic voltage and polarization voltage different(red area and green area),that is, UOCV1≠UOCVn, and SOC1≠SOCn. The difference between the voltages of cell B1 and cell Bn is given
Fig. 6. Refer to Fig. 4, the voltage of cell B1and cell Bn while discharging.
Fig. 7. The voltage of cell B1 and cell Bn while cell Bn is balanced. 4
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by
U 1 − Un = (UOCV 1 − UOCVn) − IR1 − (Up1 − Upn)
(13)
Refer to (7), when cell Bn is not isolated from the battery pack, the initial polarization voltages of cell B1 and cell Bn are the same. However, when cell Bn is isolated from the battery pack, its current is 0 but cell B1 is not. The relationship between the polarization voltage and the terminal voltage of cell B1and cell Bn is given by (14) and (15), respectively.
Up1 − Upn > 0
(14)
U 1 − Un < UOCV 1 − UOCVn
(15)
Refer to (15), the difference between the voltages of cell B1 and cell Bn is always less than the difference between OCV, which is the difference between SOC. While the voltage balancing control scheme is used and it is considered that cell Bn has been equalized, in fact, cell Bn and cell B1 do not reach a true consistency. Fig. 8. The error of G.
4. Voltage-SOC balancing control scheme
G (SOCave ) =
4.1. Principle of voltage-SOC balancing control scheme
1 f ′ (SOCave )
(25)
We rewrite (23) as
In this section, we introduce the principle of the voltage-SOC balancing control scheme, and compare it with the voltage balancing control scheme and the SOC balancing control scheme, suppose that the SOC of cell B1 is the highest and cell Bn is the lowest in the battery pack, refer to (4), obtained by lagrange mean value theorem.
ΔSOC = G (SOCave ) × ΔOCV
(26)
ΔOCV = f (SOC1) − f (SOCn)
(18)
The error of ΔSOC is proportional to G. Since the cell parameters in the battery pack obey the normal distribution [31], SOCave is approximately the SOC average of all the cells. Suppose that the SOC of each cell in the battery pack be within [SOCi, SOCi+1], and G is an increasing function, the error of G is shown in Fig. 8. G(SOCζ) and G(SOCave) are between G(SOCi) and G(SOCi+1), usually, G(SOCζ)≠G(SOCave), as shown in Fig. 8. If SOCζ = SOCi, errmax is given by
ΔSOC = SOC1 − SOCn
(19)
err max =
(20)
While ΔSOC is known, because of the Ah integral method is simple, the time of ending the equilibrium can be determined by the Ah integral method, Ah integral method is as follows:
(21)
ΔSOC =
f (SOC1) − f (SOC1) = f ′ (SOCξ ) × (SOC1 − SOCn)
(16)
SOCn < SOCξ < SOC1
(17)
ΔOCV and ΔSOC are defined as
we rewrite (16) as
ΔOCV = f ′ (SOCξ ) × SOCn The SOC of the battery pack SOCave is known, if
SOC1 − SOCn → 0 The following equation can be obtained
SOCξ = SOCave
ΔOCV f ′ (SOCave )
(23)
Refer to (23), while ΔOCV and f’(SOCave) are known, the difference in SOC between any cells can be estimated indirectly. Before cell Bn is isolated from the battery pack, cell B1 and cell Bn are in the same state, and their polarization voltages are the same, ΔOCV is given by
ΔOCV = U 1 − Un − ΔRI
1 Q
∫0
T
ηIdt
(27)
(28)
Where I is the absolute value of the current amplitude at each moment, refer to (2), and the analysis in part 2, if ΔSOC=ΔSOCB1n, the SOCs of cell B1 and cell Bn are the same. That is to say, after the cell Bn is isolated from the battery pack, if the SOC of the cell B1 drops is equal to the ΔSOC, the equalization can be considered complete. The voltage-SOC balancing control scheme proposed in this paper cannot estimate the SOC of each cell, it can estimate the difference between the SOC of the two cells. When we know the difference between the SOC of the two cells, we know which cell need to be balanced, we can know the moment when their SOC reaches the same through Ah-counting. Therefore, the method proposed in this paper can better balance the battery pack without knowing the SOC of cell. However, it must be noted that the Ah-counting method that in principle is open-loop, will inevitably be affected by measurement noise and other factors. In general, the SOC obtained by the Ah-counting is not equal to the SOC estimated by the proposed method, leading to overbalance or underbalance. If the error is small, this overbalance or underbalance is allowed, because the battery pack allows for some inconsistency. However, if the error is large, this equilibrium will likely have little effect or negative effect (if the error is greater than 100%), but this will eventually be detected by the system because its true SOC change does not reach the expected result. When the equalization is over, the system will operate again until the cell reaches the operating conditions.
(22)
We rewrite (20) as
ΔSOC =
G (SOCave ) − G (SOCi) G (SOCi)
(24)
Refer to (23) and (24), the relationship between OCV and SOC, the SOC of battery pack are known, and the terminal voltage and current of the cell are easily obtained, so that the ΔSOC can be easily obtained by the difference in the terminal voltage of the cell. However, refer to (21), the error estimated by voltage-SOC control scheme has a great relationship with the consistency of the battery pack, if the SOC of the cell in the battery pack is almost uniform, the error is small. However, the SOC difference of the cell is always present, which causes an error in the ΔSOC. The following is an analysis of the error of ΔSOC. G(SOCave) is defined as 5
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Fig. 9. The equalization process of voltage balancing control scheme, SOC balancing control scheme and voltage-SOC balancing control scheme.
4.2. Comparison and analysis with voltage balancing control scheme and SOC balancing control scheme The equalization process of voltage balancing control scheme, SOC balancing control scheme and voltage-SOC balancing control scheme is shown in Fig. 9. As shown in Fig. 9, the voltage balancing control scheme and SOC balancing control scheme respectively calculate the difference between the voltage and SOC of cells, and thereby achieving the goal of battery pack equalization. The voltage-SOC equalization method first calculates the difference between the voltages of cells, and then the SOC difference of the cell is estimated through G. Finally, the difference between the SOC of the cell is used to achieve equalization like the voltage balancing control scheme, realizing the conversion from the voltage balancing control scheme to the SOC balancing control scheme. It does not have the disadvantage that the SOC of each cell is difficult to obtain, and the parameter (voltage) is greatly affected by the state of cell. As shown in Table 1, compared with the voltage balancing control scheme, the voltage-SOC balancing control scheme only adds the calculation of G, but gets rid of the defect that the parameter of the voltage balancing control scheme is easily affected by the state of cell. Compared with the SOC balancing control scheme, the voltage-SOC balancing control scheme can obtain the difference of SOC without complex SOC estimation of cell, which has the advantages of SOC balancing control scheme to a certain extent.
Fig. 10. SOC-OCV curve. Table 2 Ohmic resistance of 5 cells.
Ohmic resistance/mΩ
Cell 1
Cell 2
Cell 3
Cell 4
Cell 5
80
80
85
70
68
Table 3 Initial voltage of 5 cells.
5. Experience 5.1. Experimental preparation
Voltage/mV
This paper chooses 18,650 lithium-ion battery produced by SAMSUNG for the experiment, whose nominal capacity and voltage are 2.2 Ah and 3.7 V, respectively. The SOC-OCV curve is shown in Fig. 10. we rewrite (4) as (29).
OCV = 14.406 × SOC5 − 43.594 × SOC 4 + 49.241 × SOC 3 − 24.926 × SOC 2 + 6.0253 × SOC + 3.0008
Cell 1
Cell 2
Cell 3
Cell 4
Cell 5
4134
4116
4135
4140
4136
The ohmic resistance of the cell changes little from 0 to 100% [21], and the ohmic resistance of each cell is replaced by the average value of the ohmic resistor. The ohmic resistance and initial voltage of the cell used in the experiment are shown in Tables 2 and 3, respectively. The MCU used in the experiment is STM32F407. To measure the
(29)
Table 1 Advantages and disadvantages of voltage balancing control scheme, SOC balancing control scheme and voltage-SOC balancing control scheme. Advantages
Disadvantages
Voltage balancing control scheme
Simple, because the voltage of each cell is easy to obtain
SOC balancing control scheme
The parameter (SOC) is less affected by the statue of cell
Voltage-SOC balancing control scheme
Simple, it is easy to obtain the difference in SOC of two cells indirectly, and the parameter (SOC) is less affected by the statue of cell
The parameter (voltage) is greatly affected by the state of cell Complex, because the SOC of each cell is not easy to obtain The estimated accuracy of the difference in SOC largely dependent on G
6
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Fig. 11. Equilibrium experiment platform.
Fig. 12. The voltage of cell 2 and cell 4.
voltage of the cell, the LTC6804 manufactured by Linear technology is used. This chip is powerful and can measure the voltage of 12 seriesconnected cells, the maximum error is 1.2 mV. A 3Ω sampling resistor is used to measure the current. The load is replaced by a 100Ω sliding rheostat. Since it is not necessary to estimate the SOC of the cell for a long time, the SOC of each cell is estimated by the Ah integral method and is regarded as the SOC true value. The voltage, SOC and current are displayed on 3.2-inch TFT color screen. The equilibrium experimental platform is shown in Fig. 11.
balancing control scheme is not satisfactory, whether at the beginning of equilibrium or at the end of equilibrium. This is because the voltage of the cell is easily affected by the state of the cell.
5.3. Verification of the performance of voltage-SOC balancing control scheme We use the voltage - SOC balancing control scheme experiment again. While ΔSOC > 1%, the cell with the lowest SOC will be isolated from the battery pack. In the experiment, 0–30 s, the battery pack is in no-load state, the difference between the terminal voltage is equal to the difference of the OCV. After 30 s, the battery pack is connected to the sliding rheostat. The voltage of 5 cells are shown in Fig. 13. As shown in Fig. 13, at 360 s, cell 2 has been equalized, and the voltage of cell 2 gradually approaches the battery pack, achieving the equilibrium goal that the voltage balancing control scheme hopes to achieve. The difference is that it has no disadvantages of the voltage balancing control scheme (as shown in Fig. 12), also, we did not achieve the above goal by estimating the SOC of all the cells, but by measuring the terminal voltage. However, the difference in voltages of cell 1, cell 3, cell 4, cell 5 is significantly increased after 30 s compared with 0 s, the initial voltage difference between cell 3 and cell 4 is 5 mV, but at 180 s, it rises to 11 mV, mainly because the ohmic resistance of cell 3 and cell 4 are different, as shown in Table 2, the ohmic resistance of cell 3 is 85mΩ, and the cell 4 is 70mΩ, cell 3 and cell 4 have different ohmic voltage drops, which makes their voltage difference. The SOC of 5 cells are as shown in Fig. 14. As shown in Fig. 14, at 360 s, the SOCs of cell 2 and cell 4 are almost
5.2. Verification of the shortcomings of voltage balancing control scheme Refer to (9), suppose that Uset = 20 mV, ΔR = 0, the SOC of cell B1 is the highest and cell Bn is the lowest in the battery pack, ΔSOC1n is defined as (30)
ΔSOC1n = ΔSOCB1 − ΔSOCBn
Refer to (29), if SOCB1 = 90%, SOCB1 = 50% and SOCB1 = 30% respectively, SOCBn and ΔSOC1n when the cell Bn will be isolated from the battery pack are shown in Table 4. As shown in Table 4, if SOCB1 = 90%, while ΔSOC1n = 2.14%, the cell Bn will be isolated from the battery pack, but when SOCB1 = 30%, ΔSOC1n will rise to 5.09%, which is about 2.38 times that of 90%. This is very unreasonable. We experimented with voltage balancing control scheme with Uset = 20 mV. Fig.12 shows the voltage of cell 2 and cell 4. To facilitate the recording of data, the equalization system refreshes every 10 s. 0 s: The voltage difference between cell 2 and cell 4 is about 24 mV, cell 2 satisfies the equalization condition, and cell 2 will be isolated from the battery pack. 10 s: Cell 2 is isolated from the battery pack and its voltage remains constant, while cell 4 supplies the load with a voltage drop of about 28 mV, so that the voltage of cell 2 is higher than cell 4. At this point, the equalization system will assume that cell 2 has been equalized. 20 s: Cell 2 supplies power to the load. However, the change of cell 2 status makes its voltage jump correspondingly. As a result, the voltage of cell 2 is still lower than that of cell 4. As shown in Table 4 and Fig. 12, the performance of the voltage Table 4 SOCBn and ΔSOC1n while SOCB1 = 90%, SOCB1 = 50% and SOCB1 = 30% respectively. SOCB1/%
SOCBn/%
ΔSOC1n/%
90 50 30
87.86 45.86 24.91
2.14 4.14 5.09
Fig. 13. The voltage of 5 cells. 7
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Fig. 17. About 30% of the battery pack, the SOC of 5 cells.
Fig. 14. The SOC of 5 cells.
Table 5 The comparison of Figs. 14–17.
U24/mV ΔOCV24/mV G/mV/% ΔSOC24c/% ΔSOC24r/% ΔSOCe/% error/%
Fig. 14
Fig. 15
Fig. 16
Fig. 17
24 24 0.071 1.704 1.7 0.004 0.24
22.3 16.1 0.1121 1.8 1.71 0.09 5.3
19.5 13.9 0.123 1.71 1.8 −0.09 −5
7.8 3.6 0.42 1.512 1.5 0.012 0.8
Fig. 15. About 83% of the battery pack, the SOC of 5 cells.
Fig. 18. ΔSOCe and error.
Fig. 16. About 53% of the battery pack, the SOC of 5 cells.
the same, which proves that the voltage-SOC balancing control scheme performs well. In order to further verify the performance of the voltageSOC balancing control scheme, about 83%, 53% and 30% of the battery pack are tested respectively. In the experiment, the equalization system is activated at a certain time, and cell 2 is balanced. In other words, before the equalization system is not enabled, the battery pack can be considered as having no equalization system. The difference between the OCV and the ΔSOC is not calculated. The time for the balanced system to work is 0 s, the SOC of each cell are shown in Figs. 15–17. As shown in Figs. 14–17, about 360 s, 420 s, 420 s and 410 s, respectively, cell 2 have been equalized, and the voltage-SOC balancing
Fig. 19. The maximum error of G.
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refer to (27), but usually such cases will not occur, so the error generated by G, which is the error of the estimated difference of SOC, will be reduced correspondingly. Moreover, if the SOC difference between cell B1 and cell B2 is 1%, even if the error of G reaches a maximum of 9%, the method proposed in this paper estimates that the SOC difference between these two cells is 1.09%, and the impact of the error is small. 6. Conclusion Due to the inconsistent state of the cell, the voltage balancing control scheme has great limitations when applied to the reconfigurable equalization circuit, for other equalization circuits, the voltage balancing control scheme also has limitations. This paper proposes a voltageSOC balancing control scheme, which only needs the difference between the terminal voltage and the SOC of battery pack, and can get the difference between the SOC of any cell, it is simple and has excellent performance, and the experimental results prove it. By using the proposed control scheme, it is possible to provide a simple, easy-to-acquire, accurate equalization parameter for the BMS (battery management system). In the future work, we will further consider the differences in the SOH (state of health) of each cell in the battery pack and the differences in the OCV-SOC curve of the cell to reduce the estimation errors caused by the voltage-SOC balancing control scheme.
Fig. 20. The maximum error of G (LFP batteries).
control scheme has better completed the task of balancing the battery pack. Then we will analyze the error of the voltage-SOC balancing control scheme. U24, ΔOCV24, ΔSOC24c, ΔSOC24r and ΔSOCe are defined as
U 24 = U 2 − U 4 ⎧ ⎪ ΔOCV 24 = U 24 − I (R2 − R 4) ⎨ ΔSOC 24c = G × ΔOCV 24 ⎪ ΔSOC 24r = SOC 2 − SOC 4 ⎩ ΔSOCe = ΔSOC 24c − ΔSOC 24r
Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No. 51677058).
(31)
Where U2, U4, R2, R4, SOC2 and SOC4 are the voltage, ohmic resistance and SOC of cell 2 and cell 4, respectively. The comparison of Figs. 14–17 are shown in Table 5. ΔSOCe and error are shown in Fig. 18. As shown in Table 5, the voltage-SOC balancing control scheme is used to estimate the difference of ΔOCV24 between cell 2 and cell 4 by ohmic resistance, voltage and current, respectively 24 mV, 16.1 mV, 13.9 mV and 3.6 mV. Of course, this is not accurate because the LTC6804 and the sampling resistor are erroneous, and we don't know the value of the ohmic resistance of each cell. According to the SOC of the battery pack, G is 0.071, 0.1121, 0.123 and 0.42, respectively, ΔSOC24c are 1.704%, 1.8%, 1.71% and 1.512%, compared with 1.7%, 1.71%, 1.8% and 1.5%, as shown in Fig. 18, the maximum error appears in Fig. 15, about 5.3%, which is equivalent to the equilibrium performance of the SOC balancing control scheme with the SOC estimation error within 5%. Although the voltage-SOC balancing control scheme performs well, there are still errors. Refer to (23), the error of the voltage-SOC balancing control scheme mainly comes from two aspects. One is the error caused by ΔOCV24, including voltage, current, and internal resistance of the cell. The second is the error caused by G. Since (21) is not satisfied, the error of ΔSOC24c estimated by (23) is shown in (27). If ΔSOC is 1%, we calculate with the data of (29) in the case of Fig. 7 and (27), the maximum error of the G is shown in Fig. 19. As shown in Fig. 19, the maximum error of G appears in about 20%, and the maximum error is about 7%, but most of it can be kept within 4%, so that the theoretical error of the voltage-SOC balancing control scheme is hardly more than 4%. We use LiFePO4 (LFP) batteries produced by LISHENG to calculate the maximum error of G, as shown in Fig. 20, the maximum error of G occurs at about 20%, and the maximum error is about to 9%, but most of it can be kept within 5%. The maximum error of G in Fig. 20 is obviously higher than that in Fig. 19, this is because the OCV-SOC curve of the LFP batteries is flat in a wide SOC range compared with experimental batteries. However, please note that in both Figs. 19 and 20, extreme cases are considered,
References [1] F. Ju, W. Deng, J. Li, Performance evaluation of modularized global equalization system for lithium-ion battery packs, IEEE Trans. Autom. Sci. Eng. 13 (April (2)) (2016) 986–996. [2] K.M. Lee, S.W. Lee, Y.G. Choi, et al., Active balancing of Li-Ion battery cells using transformer as energy carrier, IEEE Trans. Ind. Electron. 64 (February (2)) (2017) 1251–1257. [3] J. Wei, G. Dong, Z. Chen, System state estimation and optimal energy control framework for multicell lithium-ion battery system, Appl. Energy 187 (February (1)) (2017) 37–49. [4] Y. Chen, X. Liu, Y. Cui, et al., A multiwinding transformer cell-to-cell active equalization method for lithium-ion batteries with reduced number of driving circuits, IEEE Trans. Power Electron. 31 (July (7)) (2016) 4916–4929. [5] M.Y. Kim, C.H. Kim, J.H. Kim, et al., A chain structure of switched capacitor for improved cell balancing speed of lithium-ion batteries, IEEE Trans. Ind. Electron. 61 (August (8)) (2014) 3989–3999. [6] G. Gunlu, Dynamically reconfigurable independent cellular switching circuits for managing battery modules, IEEE Trans. Energy Convers. 32 (March (1)) (2016) 194–201. [7] L. He, Z. Yang, Y. Gu, et al., SoH-aware reconfiguration in battery packs, IEEE Trans. Smart Grid 9 (July (4)) (2018) 3727–3735. [8] T. Morstyn, M. Momayyezan, B. Hredzak, et al., Distributed control for state-ofcharge balancing between the modules of a reconfigurable battery energy storage system, IEEE Trans. Power Electron. 31 (November (11)) (2016) 7986–7995. [9] X. Cui, W. Shen, Y. Zhang, et al., Novel active LiFePO4 battery balancing method based on chargeable and dischargeable capacity, Comput. Chem. Eng. 97 (February (1)) (2017) 27–35. [10] C. Song, N. Lin, D. Wu, Reconfigurable battery techniques and systems: a survey, IEEE Access 4 (March (1)) (2016) 1175–1189. [11] F. Baronti, R. Roncella, R. Saletti, Performance comparison of active balancing techniques for lithium-ion batteries, J. Power Sources 267 (December (4)) (2014) 603–609. [12] D.D. Quinn, T.T. Hartley, Design of novel charge balancing networks in battery packs, J. Power Sources 240 (October (1)) (2013) 26–32. [13] L. Zhong, C. Zhang, Y. He, et al., A method for the estimation of the battery pack state of charge based on in-pack cells uniformity analysis, Appl. Energy 113 (January (1)) (2014) 558–564. [14] J. Meng, M. Ricco, G. Luo, et al., An overview and comparison of online implementable SOC estimation methods for lithium-ion battery, IEEE Trans. Ind. Appl. 54 (March (2)) (2018) 1583–1591. [15] S. Nejad, D.T. Gladwin, D.A. Stone, A systematic review of lumped-parameter equivalent circuit models for real-time estimation of lithium-ion battery states, J. Power Sources 316 (June (1)) (2016) 183–196.
9
Journal of Energy Storage 25 (2019) 100895
T. Wu, et al.
[24] L. Zheng, J. Zhu, G. Wang, et al., Model predictive control based balancing strategy for series-connected lithium-ion battery packs, 2017 19th European Conference on Power Electronics and Applications (EPE’17 ECCE Europe) (2017). [25] X. Tang, C. Zou, T. Wik, et al., Run-to-run control for active balancing of lithium iron phosphate battery packs, IEEE Trans. Power Electron. (May) (2019). [26] N. Bouchhima, M. Gossen, S. Schulte, et al., Life-time of self-reconfigurable batteries compared with conventional batteries, J. Energy Storage 15 (February (1)) (2018) 400–407. [27] Y. Wang, C. Zhang, Z. Chen, et al., A novel active equalization method for lithiumion batteries in electric vehicles, Appl. Energy 145 (May (1)) (2015) 36–42. [28] W. Huang, J.A.A. Qahouq, Energy sharing control scheme for state-of-charge balancing of distributed battery energy storage system, IEEE Trans. Ind. Electron. 62 (May (5)) (2015) 2764–2776. [29] T.H. Phung, J. Crebier, A. Chureau, et al., Optimized structure for next-to-next balancing of series-connected lithium-ion cells, IEEE Trans. Power Electron. 29 (September (9)) (2013) 4603–4613. [30] Y. Xiangwu, G. Qi, Y. Yang, et al., Study on methods for estimating the state of health of battery pack, J. Hunan Univ. 42 (February (2)) (2015) 93–99. [31] T. Baumhöfer, M. Brühl, S. Rothgang, et al., Production caused variation in capacity aging trend and correlation toinitial cell performance, J. Power Sources 247 (February (3)) (2014) 332–338.
[16] S.C. Choi, J.Y. Jeon, T.J. Yeo, et al., State-of-charge balancing control of a battery power module for a modularized battery for electric vehicle, J. Electr. Eng. Technol. 11 (November (3)) (2016) 629–638. [17] M.A. Hannan, M.M. Hoque, S.E. Peng, et al., Lithium-ion battery charge equalization algorithm for electric vehicle applications, IEEE Trans. Ind. Appl. 53 (May (3)) (2017) 2541–2549. [18] B. Dong, Y. Li, Y. Han, Parallel architecture for battery charge equalization, IEEE Trans. Power Electron. 30 (September (9)) (2017) 4906–4913. [19] Y. Shang, C. Zhang, N. Cui, et al., A cell-to-Cell battery equalizer with zero-current switching and zero-voltage gap based on quasi-resonant LC converter and boost converter, IEEE Trans. Power Electron. 30 (July (7)) (2015) 3731–3747. [20] D. Kim, J. Lee, Discharge scheduling for voltage balancing control scheme in reconfigurable battery systems, Electron. Lett. 53 (March (7)) (2017) 496–498. [21] L. He, L. Kong, S. Lin, et al., RAC: reconfiguration-assisted charging in large-scale lithium-ion battery systems, IEEE Trans. Smart Grid 7 (May (3)) (2016) 1420–1429. [22] W. Feng, L. Cheng, J. Jiuchun, et al., A New evaluation method to the consistency of lithium-ion batteries in electric vehicles, Asia-Pacific Power and Energy Engineering Conference (2012). [23] H. Weiji, Z. Changfu, Z. Chen, et al., Estimation of cell SOC evolution and system performance in module-based battery charge equalization systems, IEEE Trans. Smart Grid (Aug) (2018).
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